Equal volumes of ${\mathrm{SO}}_2$ and $\mathrm{He}$ at a temperature T and pressure P are allowed to effuse through a hole. The rate of effusion of helium is

(1) Equal to the rate of effusion of ${\mathrm{SO}}_2$

(2) Four times the rate of effusion of ${\mathrm{SO}}_2$

(3) Half of the rate of effusion of ${\mathrm{SO}}_2$

(4) Twice the rate of effusion of ${\mathrm{SO}}_2$

Flask X is filled with 20 g of ${\mathrm{CH}}_4$ gas at 100 °C and another identical flask Y with 40 g ${\mathrm{O}}_2$ gas at the same temperature. The correct statement among the following is –

1. The pressure of the gases in the two flasks is identical

2. The pressure of ${\mathrm{CH}}_4$ in flask X is higher than that of ${\mathrm{O}}_2$ in flask Y

3. The pressure of ${\mathrm{CH}}_4$ in flask X is lower than that of ${\mathrm{O}}_2$ in flask Y

4. The pressure of ${\mathrm{CH}}_4$ in flask X is half that of ${\mathrm{O}}_2$ in flask Y

A certain volume of argon gas (Mol. wt. = 40) requires 45 s to effuse through a hole at a certain pressure and temperature. The same volume of another gas of unknown molecular weight requires 60s to pass through the same hole under the same conditions of temperature and pressure. The molecular weight of the gas is

(1) 53                                 

(2) 35

(3) 71                                 

(4) 120

The rms speed of a gas molecules at temperature $27 \mathrm{K}$ and pressure $1.5$ bar is $1\times {10}^4$ cm/sec. If both temperature and pressure are raised three time, the rms speed of the gas will be

(A) $9 \times {10}^4$ cm/sec                                 

(B) $3 \times {10}^4$ cm/sec

(C) $\sqrt{3} \times {10}^4$ cm/sec                               

(D) $1 \times {10}^4$ cm/sec

The rate of effusion of helium gas at a pressure of 1000 torr is 10 torr min–1 What will be the rate of effusion of hydrogen gas at a pressure of 2000 torr at the same temperature?

(A) $20 \mathrm{torr} {\min }^{–1}$                             

(B) $40 \mathrm{torr} {\min }^{–1}$

(C) $20\sqrt{2} \mathrm{torr} {\min }^{–1}$                        

(D) $10 \mathrm{torr} {\min }^{–1}$

The van der waals' constants for a gas are : $\mathrm{a} = 4 {\mathrm{lit}}^2 \mathrm{atm} {\mathrm{mol}}^{–2}, \mathrm{b} = 0.04 \mathrm{lit} {\mathrm{mol}}^{–1}$. lts Boyle temperature is roughly

(1) ${100}^0\mathrm{C}$                        

(2) $1220 \mathrm{K}$

(3) ${1220}^0\mathrm{C}$                    

(4) $1600 \mathrm{K}$

Choose the correct statement for viscosity ($\mathrm{\eta }$) variation with T and P for an ideal gas-

1. $\mathrm{\eta }$ of a gas increases with increase in temperature (T), but it is independent of pressure

2. $\mathrm{\eta }$ of a gas decreases with increase in T and increases with increase in P

3. $\mathrm{\eta }$ of a gas is independent of temperature and pressure

4. $\mathrm{\eta }$ of a gas increases with increase in both T and P

Since the atomic weights of C, N and O are 12, 14 and 16 respectively, among the following pair, the pair that will diffuse at the same rate is$-$

(1) Carbon dioxide and nitrous oxide

(2) Carbon dioxide and nitrogen peroxide

(3) Carbon dioxide and carbon monoxide

(4) Nitrous oxide and nitrogen peroxide

Oxygen is present in 1-litre flask at a pressure of $7.6\times$ ${10}^{–10}$ mmHg.The number of oxygen molecules in the flask at $0$ $º\mathrm{C}$ is -

1. $2.686$ $\times$ ${10}^{10}$                            

2. $26.86$ $\times$ ${10}^{10}$

3. $0.626$ $\times$ ${10}^{12}$                            

4. $4.123$ $\times$ ${10}^8$

The critical temperature and critical pressure of a gas obeying van der Waals’ equation are 30ºC and 73 atm respectively. Its van der Waals’ constant, b $\left(\mathrm{in} \mathrm{litres} {\mathrm{mol}}^{-1}\right)$ is, therefore

1. 0.500                                 

2. 0.060

3. 0.265                                 

4. 0.043